"Do you have vegetarian options?" or "Does this food have eggs in it?", perhaps. (I know a few foreigners who carry business-card sized printouts with an explanation saying "Hello! The person who handed you this can't speak Japanese. She has an extremely serious medical allergy to eggs or anything containing eggs.")

Awesome suggestions and very simple to implement; look for it soon. I have many relatives who are celiacs (i.e. can't eat wheat) who have had this same problem!